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Rényi entropy and complexity measure for multivariate skew-normal distributions and related families
Javier E. Contreras-Reyes
Physics , 2014, DOI: 10.1016/j.physa.2015.03.083
Abstract: Recent studies determined that the skew-normal Shannon entropy corresponds to the difference between the common gaussian Shannon entropy and a term that depends on the skewness parameter. This allows to identify the departure from normality of a perturbed distribution. In this paper, we provide the R\'enyi entropy and complexity measure for a novel, flexible class of multivariate skew-normal distributions and their related families, as a characteristic form of the skew-gaussian Shannon entropy. We give closed expressions considering a more general class of closed skew-normal distributions and the weighted moments estimation method. In addition, closed expressions of R\'enyi entropy are presented for univariate truncated skew-normal and multivariate extended skew-normal distributions. Finally, additional inequalities for skew-normal and extended skew-normal R\'enyi and Shannon entropies are reported.
Outer rise seismicity related to the Maule, Chile 2010 megathrust earthquake and hydration of the incoming oceanic lithosphere
Moscoso,Eduardo; Contreras-Reyes,Eduardo;
Andean geology , 2012, DOI: 10.5027/andgeoV39n3-a12
Abstract: most of the recent published geodetic models of the 2010 maule, chile mega-thrust earthquake (mw=8.8) show a pronounced slip maximum of 15-20 m offshore iloca (~35°s), indicating that co-seismic slip was largest north of the epicenter of the earthquake rupture area. a secondary slip maximum 8-10 m appears south of the epicenter west of the arauco peninsula. during the first weeks following the main shock and seaward of the main slip maximum, an outer rise seismic cluster of >450 events, mainly extensional, with magnitudes mw=4-6 was formed. in contrast, the outer rise located seaward of the secondary slip maximum presents little seismicity. this observation suggests that outer rise seismicity following the maule earthquake is strongly correlated with the heterogeneous coseismic slip distribution of the main megathrust event. in particular, the formation of the outer-rise seismic cluster in the north, which spatially correlates with the main maximum slip, is likely linked to strong extensional stresses transfered from the large slip of the subducting oceanic plate. in addition, high resolution bathymetric data reveals that bending-related faulting is more intense seaward of the main maximum slip, where well developed extensional faults strike parallel to the trench axis. also published seismic constraints reveal reduced p-wave velocities in the uppermost mantle at the trench-outer rise region (7.5-7.8 km/s), which suggest serpentinization of the uppermost mantle. seawater percolation up to mantle depths is likely driven by bending related-faulting at the outer rise. water percolation into the upper mantle is expected to be more efficient during the co-seismic and early post-seismic periods of large megathrust earthquakes when intense extensional faulting of the oceanic lithosphere facilitates water infiltration seaward of the trench.
EN BUSCA DE UN MODELO BENCHMARK UNIVARIADO PARA PREDECIR LA TASA DE DESEMPLEO DE CHILE
Contreras-Reyes,Javier; Idrovo,Byron;
Cuadernos de Economía , 2011,
Abstract: in this work the precision and stability of the forecasts of chile?s unemployment rates are analyzed. said models were obtained by a family of sarima (seasonal autoregressive integrated moving average) models, between february 1986 and february 2010. the sarima projections are compared with the ones originating from univariate models, including the benchmark predictive ones. simultaneously and arfima (autoregressive fractionally integrated moving average) model was adjusted, owing to the signs of persistence that the unemployment indicator shows in its behavior; nevertheless, starting from the estimation methods developed by reisen (1994), geweke et al. (1983), and whittle (1962) integration parameters greater than 0.5 were obtained, which empirically upholds the proposal of addressing the unemployment rate as a non stationary series. the evaluation of the predictive capacity of the models is centered in the forecasts out of the sample of 1, 6, and 12 months from then on. the results indicate that the recm out of the sample of the sarima projections is less than the one from the considered univariate methods.
En busca de un modelo Benchmark univariado para predecir la tasa de desempleo
Contreras-Reyes Javier,Idrovo Byron
Cuadernos de Economía , 2011,
Abstract: En este trabajo se analiza la precisión y la estabilidad de las predicciones de la tasa de desempleo de Chile, obtenidas de una familia de modelos SARIMA, entre febrero de 1986 y febrero de 2010. Las proyecciones SARIMA son comparadas con las provenientes de modelos univariados, incluyendo los benchmarks predictivos. Simultáneamente, se ajustó un modelo ARFIMA (Autorregresive Fractionary Integrated Moving Average), debido a los signos de persistencia que muestra el indicador de desempleo en su comportamiento; sin embargo, a partir de los métodos de estimación de Reisen (1994), Geweke et al. (1983) y Whittle (1962) se obtuvieron parámetros de integración mayores que 0.5, lo que empíricamente sustenta el tratamiento de la tasa de desempleo como una serie no estacionaria. La evaluación de la capacidad predictiva de los modelos se centra en las proyecciones fuera de muestra de 1, 6 y 12 meses hacia adelante. Los resultados indican que el RECM fuera de muestra de las proyecciones SARIMA es menor que el de los métodos univariados considerados.
On the spatial correlation between areas of high coseismic slip and aftershock clusters of the Maule earthquake Mw=8.8
Javier E. Contreras-Reyes,Adelchi Azzalini
Physics , 2012,
Abstract: We study the spatial distribution of clusters associated to the aftershocks of the megathrust Maule earthquake MW 8.8 of 27 February 2010. We used a recent clustering method which hinges on a nonparametric estimation of the underlying probability density function to detect subsets of points forming clusters associated with high density areas. In addition, we estimate the probability density function using a nonparametric kernel method for each of these clusters. This allows us to identify a set of regions where there is an association between frequency of events and coseismic slip. Our results suggest that high coseismic slip spatially correlates with high aftershock frequency.
Statistical Analysis of Autoregressive Fractionally Integrated Moving Average Models
Javier E. Contreras-Reyes,Wilfredo Palma
Statistics , 2012,
Abstract: In practice, several time series exhibit long-range dependence or persistence in their observations, leading to the development of a number of estimation and prediction methodologies to account for the slowly decaying autocorrelations. The autoregressive fractionally integrated moving average (ARFIMA) process is one of the best-known classes of long-memory models. In the package afmtools for R, we have implemented some of these statistical tools for analyzing ARFIMA models. In particular, this package contains functions for parameter estimation, exact autocovariance calculation, predictive ability testing, and impulse response function, amongst others. Finally, the implemented methods are illustrated with applications to real-life time series.
Kullback–Leibler Divergence Measure for Multivariate Skew-Normal Distributions
Javier E. Contreras-Reyes,Reinaldo B. Arellano-Valle
Entropy , 2012, DOI: 10.3390/e14091606
Abstract: The aim of this work is to provide the tools to compute the well-known Kullback–Leibler divergence measure for the flexible family of multivariate skew-normal distributions. In particular, we use the Jeffreys divergence measure to compare the multivariate normal distribution with the skew-multivariate normal distribution, showing that this is equivalent to comparing univariate versions of these distributions. Finally, we applied our results on a seismological catalogue data set related to the 2010 Maule earthquake. Specifically, we compare the distributions of the local magnitudes of the regions formed by the aftershocks.
Surface Screening in the Casimir Force
Ana M. Contreras-Reyes,W. Luis Mochán
Physics , 2005, DOI: 10.1103/PhysRevA.72.034102
Abstract: We calculate the corrections to the Casimir force between two metals due to the spatial dispersion of their response functions. We employ model-independent expressions for the force in terms of the optical coefficients. We express the non-local corrections to the Fresnel coefficients employing the surface $d_\perp$ parameter, which accounts for the distribution of the surface screening charge. Within a self-consistent jellium calculation, spatial dispersion increases the Casimir force significatively for small separations. The nonlocal correction has the opposite sign than previously predicted employing hydrodynamic models and assuming abruptly terminated surfaces.
Growth curve based on scale mixtures of skew-normal distributions to model the age-length relationship of Cardinalfish (Epigonus Crassicaudus)
Javier E. Contreras-Reyes,Reinaldo B. Arellano-Valle
Statistics , 2012,
Abstract: Our article presents a robust and flexible statistical modeling for the growth curve associated to the age-length relationship of Cardinalfish (Epigonus Crassicaudus). Specifically, we consider a non-linear regression model, in which the error distribution allows heteroscedasticity and belongs to the family of scale mixture of the skewnormal (SMSN) distributions, thus eliminating the need to transform the dependent variable into many data sets. The SMSN is a tractable and flexible class of asymmetric heavy-tailed distributions that are useful for robust inference when the normality assumption for error distribution is questionable. Two well-known important members of this class are the proper skew-normal and skew-t distributions. In this work emphasis is given to the skew-t model. However, the proposed methodology can be adapted for each of the SMSN models with some basic changes. The present work is motivated by previous analysis about of Cardinalfish age, in which a maximum age of 15 years has been determined. Therefore, in this study we carry out the mentioned methodology over a data set that include a long-range of ages based on an otolith sample where the determined longevity is higher than 54 years.
Discriminant functions arising from selection distributions: theory and simulation
Reinaldo B. Arellano-Valle,Javier E. Contreras-Reyes
Statistics , 2014,
Abstract: The assumption of normality in data has been considered in the field of statistical analysis for a long time. However, in many practical situations, this assumption is clearly unrealistic. It has recently been suggested that the use of distributions indexed by skewness/shape parameters produce more exibility in the modelling of different applications. Consequently, the results show a more realistic interpretation for these problems. For these reasons, the aim of this paper is to investigate the effects of the generalisation of a discrimination function method through the class of multivariate extended skew-elliptical distributions, study in detail the multivariate extended skew-normal case and develop a quadratic approximation function for this family of distributions. A simulation study is reported to evaluate the adequacy of the proposed classi?cation rule as well as the performance of the EM algorithm to estimate the model parameters.
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